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Geostatistics
Geostatistics is a branch of statistics focusing on spatial or spatiotemporal datasets. Developed originally to predict probability distributions of ore grades for mining operations, it is currently applied in diverse disciplines including petroleum geology, hydrogeology, hydrology, meteorology, oceanography, geochemistry, geometallurgy, geography, forestry, environmental control, landscape ecology, soil science, and agriculture (esp. in precision farming). Geostatistics is applied in varied branches of geography, particularly those involving the spread of diseases (epidemiology), the practice of commerce and military planning (logistics), and the development of efficient spatial networks. Geostatistical algorithms are incorporated in many places, including geographic information systems (GIS). Background Geostatistics is intimately related to interpolation methods, but extends far beyond simple interpolation problems. Geostatistical techniques rely on statistical models ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Variogram
In spatial statistics the theoretical variogram 2\gamma(\mathbf_1,\mathbf_2) is a function describing the degree of spatial dependence of a spatial random field or stochastic process Z(\mathbf). The semivariogram \gamma(\mathbf_1,\mathbf_2) is half the variogram. In the case of a concrete example from the field of gold mining, a variogram will give a measure of how much two samples taken from the mining area will vary in gold percentage depending on the distance between those samples. Samples taken far apart will vary more than samples taken close to each other. Definition The semivariogram \gamma(h) was first defined by Matheron (1963) as half the average squared difference between the values at points (\mathbf_1 and \mathbf_2) separated at distance h. Formally :\gamma(h)=\frac\iiint_V \left (M+h) - f(M) \right2dV, where M is a point in the geometric field V, and f(M) is the value at that point. The triple integral is over 3 dimensions. h is the separation distance (e.g., ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Geography
Geography (from Greek: , ''geographia''. Combination of Greek words ‘Geo’ (The Earth) and ‘Graphien’ (to describe), literally "earth description") is a field of science devoted to the study of the lands, features, inhabitants, and phenomena of Earth. The first recorded use of the word γεωγραφία was as a title of a book by Greek scholar Eratosthenes (276–194 BC). Geography is an all-encompassing discipline that seeks an understanding of Earth and its human and natural complexities—not merely where objects are, but also how they have changed and come to be. While geography is specific to Earth, many concepts can be applied more broadly to other celestial bodies in the field of planetary science. One such concept, the first law of geography, proposed by Waldo Tobler, is "everything is related to everything else, but near things are more related than distant things." Geography has been called "the world discipline" and "the bridge between the human an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Geographic Information Systems
A geographic information system (GIS) is a type of database containing geographic data (that is, descriptions of phenomena for which location is relevant), combined with software tools for managing, analyzing, and visualizing those data. In a broader sense, one may consider such a system to also include human users and support staff, procedures and workflows, body of knowledge of relevant concepts and methods, and institutional organizations. The uncounted plural, ''geographic information systems'', also abbreviated GIS, is the most common term for the industry and profession concerned with these systems. It is roughly synonymous with geoinformatics and part of the broader geospatial field, which also includes GPS, remote sensing, etc. Geographic information science, the academic discipline that studies these systems and their underlying geographic principles, may also be abbreviated as GIS, but the unambiguous GIScience is more common. GIScience is often considered a subdisc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Geometallurgy
Geometallurgy relates to the practice of combining geology or geostatistics with metallurgy, or, more specifically, extractive metallurgy, to create a spatially or geologically based predictive model for mineral processing plants. It is used in the hard rock mining industry for risk management and mitigation during mineral processing plant design. It is also used, to a lesser extent, for production planning in more variable ore deposits. There are four important components or steps to developing a geometallurgical program,: *the geologically informed selection of a number of ore samples *laboratory-scale test work to determine the ore's response to mineral processing unit operations *the distribution of these parameters throughout the orebody using an accepted geostatistical technique *the application of a mining sequence plan and mineral processing models to generate a prediction of the process plant behavior Sample selection The sample mass and size distribution requirements ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Inverse Distance Weighting
Inverse distance weighting (IDW) is a type of deterministic method for multivariate interpolation with a known scattered set of points. The assigned values to unknown points are calculated with a weighted average of the values available at the known points. This method can also be used to create spatial weights matrices in spatial autocorrelation analyses (e.g. Moran's ''I''). The name given to this type of method was motivated by the weighted average applied, since it resorts to the inverse of the distance to each known point ("amount of proximity") when assigning weights. Definition of the problem The expected result is a discrete assignment of the unknown function u in a study region: :u(x): x \to \mathbb, \quad x \in \mathbf \sub \mathbb^n, where \mathbf is the study region. The set of N known data points can be described as a list of tuples: : x_1, u_1), (x_2, u_2), ..., (x_N, u_N) The function is to be "smooth" (continuous and once differentiable), to be exact (u(x_i) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Precision Farming
Precision agriculture (PA) is a farming management strategy based on observing, measuring and responding to temporal and spatial variability to improve agricultural production sustainability. It is used in both crop and livestock production. Precision agriculture often employs technologies to automate agricultural operations, improving their diagnosis, decision-making or performing. First conceptual work on PA and practical applications go back in the late 1980s. The goal of precision agriculture research is to define a decision support system (DSS) for whole farm management with the goal of optimizing returns on inputs while preserving resources. Among these many approaches is a phytogeomorphological approach which ties multi-year crop growth stability/characteristics to topological terrain attributes. The interest in the phytogeomorphological approach stems from the fact that the geomorphology component typically dictates the hydrology of the farm field. The practice of pre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Agriculture
Agriculture or farming is the practice of cultivating plants and livestock. Agriculture was the key development in the rise of sedentary human civilization, whereby farming of domesticated species created food surpluses that enabled people to live in cities. The history of agriculture began thousands of years ago. After gathering wild grains beginning at least 105,000 years ago, nascent farmers began to plant them around 11,500 years ago. Sheep, goats, pigs and cattle were domesticated over 10,000 years ago. Plants were independently cultivated in at least 11 regions of the world. Industrial agriculture based on large-scale monoculture in the twentieth century came to dominate agricultural output, though about 2 billion people still depended on subsistence agriculture. The major agricultural products can be broadly grouped into foods, fibers, fuels, and raw materials (such as rubber). Food classes include cereals ( grains), vegetables, fruits, cooking oils, m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Neighbourhood (mathematics)
In topology and related areas of mathematics, a neighbourhood (or neighborhood) is one of the basic concepts in a topological space. It is closely related to the concepts of open set and interior. Intuitively speaking, a neighbourhood of a point is a set of points containing that point where one can move some amount in any direction away from that point without leaving the set. Definitions Neighbourhood of a point If X is a topological space and p is a point in X, then a of p is a subset V of X that includes an open set U containing p, p \in U \subseteq V \subseteq X. This is also equivalent to the point p \in X belonging to the topological interior of V in X. The neighbourhood V need be an open subset X, but when V is open in X then it is called an . Some authors have been known to require neighbourhoods to be open, so it is important to note conventions. A set that is a neighbourhood of each of its points is open since it can be expressed as the union of open ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Cumulative Distribution Function
In probability theory and statistics, the cumulative distribution function (CDF) of a real-valued random variable X, or just distribution function of X, evaluated at x, is the probability that X will take a value less than or equal to x. Every probability distribution supported on the real numbers, discrete or "mixed" as well as continuous, is uniquely identified by an ''upwards continuous'' ''monotonic increasing'' cumulative distribution function F : \mathbb R \rightarrow ,1/math> satisfying \lim_F(x)=0 and \lim_F(x)=1. In the case of a scalar continuous distribution, it gives the area under the probability density function from minus infinity to x. Cumulative distribution functions are also used to specify the distribution of multivariate random variables. Definition The cumulative distribution function of a real-valued random variable X is the function given by where the right-hand side represents the probability that the random variable X takes on a value less ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Potentiometric Surface
A potentiometric surface is the imaginary plane where a given reservoir of fluid will "equalize out to" if allowed to flow. A potentiometric surface is based on hydraulic principles. For example, two connected storage tanks with one full and one empty will gradually fill/drain to the same level. This is because of atmospheric pressure and gravity. This idea is heavily used in city water supplies - a tall water tower containing the water supply has a great enough potentiometric surface to provide flowing water at a decent pressure to the houses it supplies. For groundwater "potentiometric surface" is a synonym of "piezometric surface" which is an imaginary surface that defines the level to which water in a confined aquifer would rise were it completely pierced with wells. If the potentiometric surface lies above the ground surface, a flowing artesian well results. Contour maps and profiles of the potentiometric surface can be prepared from the well data. See also * Hydraulic head ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Nearest-neighbor Interpolation
Nearest-neighbor interpolation (also known as proximal interpolation or, in some contexts, point sampling) is a simple method of multivariate interpolation in one or more dimensions. Interpolation is the problem of approximating the value of a function for a non-given point in some space when given the value of that function in points around (neighboring) that point. The nearest neighbor algorithm selects the value of the nearest point and does not consider the values of neighboring points at all, yielding a piecewise-constant interpolant. The algorithm is very simple to implement and is commonly used (usually along with mipmapping) in real-time 3D rendering to select color values for a textured surface. Connection to Voronoi diagram For a given set of points in space, a Voronoi diagram is a decomposition of space into cells, one for each given point, so that anywhere in space, the closest given point is inside the cell. This is equivalent to nearest neighbour interpolation, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Bilinear Interpolation
In mathematics, bilinear interpolation is a method for interpolating functions of two variables (e.g., ''x'' and ''y'') using repeated linear interpolation. It is usually applied to functions sampled on a 2D rectilinear grid, though it can be generalized to functions defined on the vertices of (a mesh of) arbitrary convex quadrilaterals. Bilinear interpolation is performed using linear interpolation first in one direction, and then again in the other direction. Although each step is linear in the sampled values and in the position, the interpolation as a whole is not linear but rather quadratic in the sample location. Bilinear interpolation is one of the basic resampling techniques in computer vision and image processing, where it is also called bilinear filtering or bilinear texture mapping. Computation Suppose that we want to find the value of the unknown function ''f'' at the point (''x'', ''y''). It is assumed that we know the value of ''f'' at the four points ''Q''11 = ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |